Seminars
Seminars
This page is for the Brown-Ozawa reading seminar that I co-organized at the University of Houston with Randy Pham.
The first week will review C*-theory from [Murphy]. The following weeks will cover material from [Brown-Ozawa].
Meeting place: Fridays, sometime between 2pm and 5pm, in PGH 648.
September 12th: Murphy, chapters 2 and 3.
The GNS construction and the universal representation.
Speaker: Theodore Vo
September 19th: Brown-Ozawa, sections 1.3-1.5.
The bidual of a C*-algebra and Tomiyama's theorem.
Speaker: Joel Sleeba
September 26th: Brown-Ozawa, sections 2.1, 2.3, 2.4.
Nuclearity and exactness.
Speaker: Caleb McClure
October 3rd: Brown-Ozawa, 2.5 and 2.6.
Group C*-algebras and amenability.
Speaker: Christiaan Hendrik Pretorius
October 10th: Interlude (virtual, scheduling conflicts)
Kadison's transitivity theorem and excision.
Speaker: Joseph Gondek
October 17th: Brown-Ozawa, 3.3 and 3.4.
C*-tensor norms and Takesaki's theorem.
Speaker: Joseph Gondek
October 24th: Brown-Ozawa, 3.5.
Continuity of completely positive maps.
Speaker: Nazmul Alam
October 31st: Brown-Ozawa, 3.6.
Uniqueness of C*-tensor norms for nuclear C*-algebras and related results.
Speaker: Caleb Barnett
Further talks to be determined.
[Murphy] Murphy, G., C*-algebras and operator theory, 1990.
[Brown-Ozawa] Brown, N., Ozawa, N., C*-algebras and finite-dimensional approximations, 2008.
This page is for the student-run Abstract Harmonic Analysis group study that I organized at Carleton between July and October 2023.
Our references for the Fall 2023 AHA seminar are [Folland] and various appendices of [Bekka]. The last talk followed [H-R] for Tannaka-Krein duality.
Meeting place: HP 4325. Fridays, 3pm-4:30pm. The last two talks will take place from 3pm-6pm.
September 15th: A review of classical Fourier analysis.
Speaker: Joseph Gondek
September 22nd: Folland 3.1; Bekka A.1, A.2, A.4.
Unitary representations and Schur's Lemma.
Speaker: Yaren Zhang
September 29th: Folland 3.2; Bekka F.4.
The group algebra. C*-algebras from locally compact groups.
Speaker: Finlay Rankin
October 6th: Folland 3.14-3.20; Bekka C.1.1-C.1.4, C.4.1-C.4.10, C.4.13.
Functions of positive type. The GNS construction.
Speaker: Quintin Trayling
October 13th: Folland 3.21-3.34; Bekka C.5.
The Gelfand-Raikov Theorem.
Speaker: Soroush Kazemi
All talks below this point take place from 3pm-6pm in HP 4325. Food, caffeine, and breaks will be provided to both the audience and the speaker.
October 20th, 3-hour talk: Folland, Chapter 4.
Analysis on locally compact abelian groups. The dual group, Fourier transform, Pontrjagin-van Kampen duality, and examples.
Speaker: Finlay Rankin
October 27th, 3-hour talk: Folland, Chapter 5.
Analysis on compact groups. The Peter-Weyl theorem, Krein algebras, Tannaka-Krein duality, and examples.
Speaker: Joseph Gondek (notes)
[Bekka] Bekka, B., Kazhdan's Property (T), 2007.
[Folland] Folland, G., A Course in Abstract Harmonic Analysis (2nd ed.), 2015.
[H-R] Hewitt, E., Ross, K., Abstract Harmonic Analysis: Volume II, 1970.
The Summer 2023 seminar was co-organized by Yaren Zhang and I. Our references were [Bray] and Chapter 2 of [Folland].
July 13th - Bray, Section 2.1.
Speaker: Joseph Gondek (notes)
July 20th - Bray, Section 2.2.
Speaker: Yaren Zhang
July 27th - Bray, Section 2.3.
Speaker: Brian Lin
August 3rd - Bray, Sections 2.5 and 2.6.
Speaker: Karl Roscoe
August 10th - Bray, Sections 5.1 and 5.3.
Speaker: Joseph Gondek (notes)
August 17th - Bray, Section 5.2; Folland, Section 2.3.
Speaker: Stephen Tran
August 24th - Folland, Section 2.5.
Speaker: Soroush Kazemi
August 31st - Folland, Section 2.6.
Speaker: Finlay Rankin
[Bray] Bray, T., An Introduction to Topological Groups, 2021.
[Folland] Folland, G., A Course in Abstract Harmonic Analysis (2nd ed.), 2015.
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